If we have an AR(1) process, i.e: $X_{t+1} = \alpha X_t + e_{t+1}$ then what is its Markov Chain transition density?
We know that for a Markov chain, the following holds:
$P(X_{t+1}\leq x_{t+1} \mid ...

I am trying to find the probability of the following question:
Cans of regular Coke are labeled as containing 12 oz.
Statistics students weighed the contents of 7 randomly chosen cans, and found the ...

There are $m$ white balls and $n$ black balls in a box. Balls are randomly drawn from the box with no return. Denote $X_1$ : number of white balls that been drawn before the first black. For $2 \leq i ...

I have a normal distribution of independent variables, and there are a specific number of samples to this distribution: say 1 million samples. A function is set by the largest value of these million ...

I searched the web, taking advantage of several search approaches; however, due to redundancy of the existing information about Bayes estimator of one unknown parameter of random variables (either in ...

Let $(aX + bY)$ be a truncated normal and assume $X,Y$ are both identically distributed (but necessarily NOT independent) what is the distribution of $X$ and $Y$? More importantly can the pdf of $X$ ...

The number of customers arriving at a bank counter is in accordance with a Poisson distribution with mean rate of 5 customers in 3 minutes. Service time at the counter follows exponential distribution ...

When $X,Y$ are iid random variables, uniformly distributed on $[0,1]$, then $Z=X*Y$ has the density $-\log(z)$, as it is shown here:
product distribution of two uniform distribution, what about 3 or ...

A circus performer who gets shot from a cannon is supposed to land in a safety net positioned at the other end of the arena. The distance he travels is normally distributed with a mean of 140 feet and ...

The probability that a randomly selected $2$ year old male feral will live to be $3$ years old is $0.82666$.
(a) what is the probability that two randomly selected $2$ year old male feral cats will ...

I'm thinking about a set of n users on Facebook. Between each of the $\binom{n}{2}$ pairs of distinct friends, lets say an edge (indicating that the two people are friends) is independently present ...

I'm have a random vector $\bf a$ with binary entries, $a_i \in \{0,1\}$. The probability distribution $P({\bf a})$ is not fully specified, but I have the marginals $p_i$, which are the probabilities ...

The probability of a man hitting a target is $2/3$. If he doesn't stop shooting until he hits the target for the first time, a) What is the probability of taking 5 shots to hit the target? b) Which is ...

I have a project in which there exist $N$ Beta-distributed Random variables each of which should be estimated, having a sample for each of them. The sample domain is $\{0.1,0.3,0.5,0.7,0.9\}$ and the ...

I'm trying to use the Chi-Square test to find the significance of data that suffers from the multiple testing problem. Because I have this multiple testing problem, the required p-value to view a test ...